The entire treasury of the Alpha club, consisting of $240, was to be divided into equal shares for each club member. When it was discovered that one member was not eligible for a share, the share of the remaining members increased by $1. How many eligible members got a share of the $240?
Let's break down the problem step by step.
We know that the total treasury of the Alpha club is $240. Let's assume there are "N" members in the club.
If the money was divided equally among all N members, each member would receive $240/N.
But here's the important part: when it was discovered that one member was not eligible for a share, the share of the remaining members increased by $1.
So, the remaining members now receive $240/N + $1 each.
To figure out the number of eligible members, we need to find when the increased share is equal to the original share ($240/N).
Setting up the equation:
$240/N + $1 = $240/N
To solve for N, we can simplify the equation:
$1 = $0
As you can see, this equation doesn't make sense. It means that there is no value of N for which the increased share is equal to the original share.
Therefore, according to the given information, there is no way to determine the number of eligible members who got a share of the $240.
OOOH HAHAHAHHA
let m equal the number of members .. so m - 1 equals eligible members
(240 / m) + 1 = 240 / (m - 1)
240 m - 240 + m^2 - m = 240 m ... m^2 - m - 240 = 0
(m + 15)(m - 16) = 0